Problem: $A$ $B$ $C$ If: $ BC = 8x + 7$, $ AB = 2x + 2$, and $ AC = 39$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {2x + 2} + {8x + 7} = {39}$ Combine like terms: $ 10x + 9 = {39}$ Subtract $9$ from both sides: $ 10x = 30$ Divide both sides by $10$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $BC$ $ BC = 8({3}) + 7$ Simplify: $ {BC = 24 + 7}$ Simplify to find ${BC}$ : $ {BC = 31}$